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Related Concept Videos

Singularity Functions for Bending Moment01:18

Singularity Functions for Bending Moment

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Singularity functions simplify the representation of bending moments in beams subjected to discontinuous loading, allowing the use of a single mathematical expression. For a supported beam AB, with uniform loading from its midpoint M to the right side end B, the approach involves conceptual 'cuts' at specific points to determine the bending moment in each segment. By cutting the beam at a point between A and M, the bending moment for the segment before reaching midpoint M is represented...
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Bending of Curved Members - Strain Analysis01:14

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The mechanics of deformation in curved members, such as beams or arches, under bending moments, involve complex responses. When such a member, symmetric about the y-axis and shaped like a segment of a circle centered at point C, is subjected to equal and opposite forces, its curvature and surface lengths change significantly. This alteration results in the shift of the curvature's center from C to C', indicating a tighter curve.
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Bending of Material: Problem Solving01:09

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In this lesson, determine the ratio of the maximum bending moments applied to two metal pipes, given that both pipes can withstand a maximum stress of 100 MPa. Both pipes have an outer radius of 1.8 cm. Pipe A has an inner radius of 1.5 cm, and Pipe B has an inner radius of 1 cm. The ratio of the maximum bending moment applied to two metallic pipes, each with a different inner and outer radius, is determined by considering their dimensions. The inner radius of the first pipe is 1.5 cm, and for...
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Shear and Bending Moment Diagram: Problem Solving01:24

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When analyzing a beam supporting concentrated loads and a distributed load, drawing the shear and bending moment diagrams is essential. These diagrams help understand the internal forces and moments acting on the beam, which is crucial for designing safe and efficient structures. Follow these steps to create the shear and bending moment diagrams:
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Unsymmetric Bending - Angle of Neutral Axis01:15

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Unsymmetrical bending occurs when a structural member is subjected to bending moments in a plane that does not align with the member's principal axes. This scenario typically arises in beams and other structural components when loads are applied at non-ideal angles, introducing complexities in stress analysis.
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A bending moment diagram is a graphical representation of the bending moments experienced by a beam under load along the beam length. It is an essential tool for engineers and designers to analyze structures and ensure they can withstand applied forces. The steps to create the bending moment diagram for a beam are listed below.
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A branch-and-Benders-cut algorithm for a bi-objective stochastic facility location problem.

Sophie N Parragh1, Fabien Tricoire2, Walter J Gutjahr3

  • 1Institute of Production and Logistics Management, Johannes Kepler University Linz, Altenberger Straße 69, 4040 Linz, Austria.

OR Spectrum : Quantitative Approaches in Management
|June 8, 2022
PubMed
Summary
This summary is machine-generated.

This study addresses the bi-objective stochastic facility location problem, crucial for disaster relief and public facility planning. It introduces an efficient Branch-and-Benders-cut method for optimizing cost and demand coverage under uncertainty.

Keywords:
Benders decompositionBi-objective optimizationBranch and boundL-shaped methodPareto efficiencyStochastic optimization

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Area of Science:

  • Operations Research
  • Applied Mathematics
  • Optimization

Background:

  • Real-world optimization often involves multiple objectives and uncertain parameters.
  • Applications in disaster relief and public facility location highlight the need for robust models.

Purpose of the Study:

  • To model and solve a bi-objective stochastic facility location problem.
  • To optimize both cost and covered demand when demand is uncertain but its distribution is known.

Main Methods:

  • Utilized a Benders' type decomposition approach (L-shaped method) for stochastic programming.
  • Embedded the L-shaped method within a branch-and-bound framework for bi-objective integer optimization.
  • Analyzed and compared various cut generation schemes for lower bound set computations.

Main Results:

  • Identified the best-performing approach among different cut generation schemes.
  • Compared the novel Branch-and-Benders-cut approach against a standard branch-and-bound method using the deterministic equivalent formulation.

Conclusions:

  • The proposed Branch-and-Benders-cut method offers an effective solution for bi-objective stochastic facility location problems.
  • The study provides insights into optimizing facility location strategies for scenarios with uncertain demand.